Ratio distribution is a probability distribution representing the ratio of two random variables, each usually having a known distribution. Currently, there are results when the random variables in the ratio follow (not necessarily the same) Gaussian, Cauchy, binomial or uniform distributions. In this paper we consider a case, where the random variables in the ratio are joint binomial components of a multinomial distribution. We derived formulae for mean and variance of this ratio distribution using a simple Taylor-series approach and also a more complex approach which uses a slight modification of the original ratio. We showed that the more complex approach yields better results with simulated data. The presented results can be directly applied in the computation of confidence intervals for ratios of multinomial proportions. AMS Subject Classification: 62E20

中文翻译：

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来自多项式分布类别的比例比率的均值和方差

比率分布是表示两个随机变量的比率的概率分布，每个变量通常具有已知的分布。当前，当比率中的随机变量遵循（不一定相同）高斯，柯西，二项式或均匀分布时，就会有结果。在本文中，我们考虑一种情况，其中比率中的随机变量是多项式分布的联合二项式分量。我们使用简单的泰勒级数方法以及使用稍微修改原始比率的更复杂的方法得出该比率分布的均值和方差的公式。我们显示，使用模拟数据，更复杂的方法会产生更好的结果。提出的结果可以直接用于多项比例比例的置信区间的计算中。